Doubling of a certificate

Question

The doubling time of the balance for a money market certificate of deposit (CD) is 25 years. By what factor does it grow in 60 years?

Answer 1

First use the continuous growth equation A = Pe^rt.  Allow the intial value P to be $1, then double value for P is 2.

 

                                     2 = (1)e^(25r) 

                                      2 = e^(25r)

                                   ln 2 = ln e^(25r)

                                   ln 2 = (25r) ln e    since ln e = 1 we have

                                     ln 2 = 25r

                                     (ln 2)/25 = r ≈ 0.277258872

 

Now use A = Pe^rt ,       A = (1)e^{(0.277258872•60)}

                                  A ≈ 5.27

 

The money market certificate will grow by a factor of ≈ 5.27